9-1

9-1 Solving Right Triangles

In order to solve a right triangle, we use SOHCAHTOA:
sine(theta)=opposite/hypotenuse cosine(theta)=adjacent/hypotenuse tangent(theta)=opposite/adjacent
You can only use these formulas for right triangles. You can use any angle except the 90 degree.

Example 1:

• cosine 25 degrees=c/8


• c=16.314


• sin 25 degrees=18/b


• b=24.267

Example 2:

• cos 37 degrees=25/x


• x=31.303


• tan 37 degrees=y/25


• y=18.839

Example 3: Find the measures of the acute angles of a 3-4-5 right triangle.

• sin x=3/5


• x=sin^-1(3/5)


• =36.861 degrees


• tan x=4/3


• x=tan^-1(4/3)


• =53.130 degrees

Example 4: The legs of an isosceles triangle are each 21 cm long and the angle between them has measure 52 degrees. What is the length of the third side?

• sin 26 degrees=x/21


• x=9.206 cm


• 9.206(2)


• =18.412 cm

Example 5: In Triangle ABC,

• sin 25 degrees=b/18


• b=7.607


• cos 25 degrees=c/18


• c=16.314

-Jordan Duhon